deltahedron

A polyhedron whose faces consist of equilateral
triangles that are all the same size. Although there are an infinite number
of different deltahedra, only eight of them are convex,
as O. Rausenberger first showed in 1915. Among this group of eight, faces
made of coplanar equilateral triangles
sharing an edge (such as the rhombic dodecahedron) aren't allowed. The eight
convex deltahedra have 4, 6, 8, 10, 12, 14, 16, and 20 faces.